Early on in this illuminating and humane book, Sarah Bakewell announces that it is not only about about Michel de Montaigne the man and the writer, but also "about Montaigne, the long party". The phrase is both apt and happy. The subject of this "Life of Montaigne in one question and twenty attempts at an answer" was pleased with his Essays. "It is," he says, "the only book in the world of its kind", and I suppose it remains so even today.

Rousseau made a similar claim for his Confessions but its very title placed him firmly centre-stage - he, not his book, was the unique object - while the Essays put Montaigne on a level with the reader. He doesn't instruct or boast but asks us to join him in looking at himself, wondering how one should live and hopefully becoming "reconciled to this colicky life". An essay is a gesture of imperfection, an essai - an "attempt" or a "trial". Montaigne's signature phrase is "but I don't know." He may be wrong. We may be right. It's all an ongoing conversation, across time.

Hence the "long party". A common remark by Montaigne's readers has been that it felt as if you'd written it yourself. Our receptions of him change according to the times. His Enlightenment readers read in Montaigne justification for their own Enlightenment; Romantics saw their exalted super-sensibilities reflected; various bowdlerisations recast the Essays in a form suitable for the emerging brash timidity of the Victorian consciousness.

Nietzsche read him with the same (and entirely different) delight as Shakespeare had. Semioticians, deconstructionists and literary psychoanalysts have all had a pop at Montaigne and found exactly what they expected. If there's one word that suits his style, it's that coinage of the 20th-century guru of deconstruction, Jacques Derrida: the punning différance, a slippery hybrid of differentiation and deferral.

Montaigne was an expert at both, but deferral always won. Whether he's writing about cannibals, thumbs, experience, glory or drunkenness, there's always a side-issue, a backwater, a beckoning digression, and he takes them joyfully. Within moments of starting to write "On Vanity", he's remembering a man who had seven or eight days' worth of filled chamber pots by him at all times and "communicated his life by the workings of his belly." Before long he's telling us how he'd have liked a son-in-law; later, he muses on cheating servants, astrologers, courtesy, Lacedaemonians, and Paris.

He boasts of his endurance in the saddle, complains of the kidney-stones which he inherited from his father (and which eventually put an end to him), confesses his horror of early rising, speculates on how people can read his inmost self in his books, accuses Plutarch of often forgetting what he's writing about, discovers himself "full of inanity and foppery" and ends by telling his readers that they, like he, will, if they look into themselves, find they are "after all, the fool of the farce."

Sarah Bakewell embraces this exuberant digressiveness with delight and obvious profound affection. It's rare to come across a biographer who remains so deliciously fond of her subject. She turns her extensive research towards making the reader not just know Montaigne but love him. And how can we refuse to love a man who turned to and in many ways invented the essay because his mind could "never gain a firm footing", so that his ideas were always "in apprenticeship and on trial"?

His digressions, his différances, extended to the composition of his entire oeuvre, which "grew by slow encrustation, like a coral reef, from 1572 to 1592. The only thing that eventually stopped it was Montaigne's death." He would return again and again to an essay, amending it as his views changed.

Montaigne was one of us, a work-in-progress. But his writing was, in part at least, prompted by another work-in-progress, cruelly cut short, when his life's friend Étienne de La Boétie died of the plague, aged 33. Asked why they were so fond of each other, Montaigne could only stutter, "Because it was him. Because it was me." If there was ever a better description of love, I haven't read it. Putting La Boétie's papers in order seemed to set Montaigne in the grip of writing; his loss was our gain.

Bakewell pulls off the great trick of writing Montaigne in both the context of his own time and of subsequent ages. If you know his work, How to Live will delight and illuminate. If you don't, the book stands splendidly alone, as a picture of a man worth knowing, and will certainly turn you to the Essays.

In short, Montaigne has here the biography he deserves, and would have enjoyed its unconventional structure. Bakewell treats his life and work thematically, each chapter taking one element of how to live from his own writing - for example, "Pay attention," "Survive love and loss," "See the world".

The result works beautifully. Bakewell makes no attempt to efface herself, yet her vivid presence never obscures his. It's rather like having a conversation about a mutual friend, with one who knows him much better.

Perhaps it's in the end about focus. Montaigne knew about that, too. "When I dance, I dance. When I sleep, I sleep," he wrote. And what a fine dance it was.